1. Pinning down the J PC values of the X(3872) K. Miyabayashi for S.K. Choi & S.L. Olsen Feb, 2005 Belle Analysis & Software Meeting

2. J PC possibilities for J ≤ 2 0 - - exotic violates parity 0 -+ (  c ” ) 0 ++ DD allowed (  c0 ’ ) 0 +- exotic DD allowed 1 - - DD allowed (  (3S)) 1 -+ exotic DD allowed 1 ++ (  c1 ’ ) 1 +- (h c ’ ) 2- -(2)2- -(2) 2 - + (  c2 ) 2 ++ DD allowed  c2 ’ ) 2 +- exotic DD allowed

3. P-viol’n & DD -allowed J PC s unlikely (reduce type size of these entries by x1/2) 0 - - exotic violates parity 0 -+ (  c ” ) 0 ++ DD allowed (  c0 ’ ) 0 +- exotic DD allowed 1 - - DD allowed (  (3S)) 1 -+ exotic DD allowed 1 ++ (  c1 ’ ) 1 +- (h c ’ ) 2- -(2)2- -(2) 2 - + (  c2 ) 2 ++ DD allowed  c2 ’ ) 2 +- exotic DD allowed

4. Use e7 – e37 data (include B  K S     J/  ) Signal (47 ev) Sidebands (114/10 = 11.4 ev)

5. Follow advice from Sherlock Holmes: Eliminate all other factors, & the one that remains must be the truth.* *The sign of four

6. Areas of investigation Angular correlations Search for radiative decays Fits to the M(  ) distribution

7. Angular Correlations

8. Strategy: for each J PC, find a distrib  0 if we see any events there, we can rule it out  example 1 -- : sin 2  K  K compute angles in J/  restframe D.V. Bugg hep-ph/0410168v2  ’  2 /dof = 8.9/9 Use  ’ to check accept.  ’ is 1 --

9. |cos  Kl | for X(3872) events X(3872) is not 1 -- ! expect 2~3evts/bin background scaled from sidebands fit with sin 2  Kl + bkgd  2 /dof = 60.3/9 see 8 evts/bin

10. 1 +- and 2 -- use J/  helicity angle  J/  K X J/   J/  |cos  J/  | For the  ’      J/ , this should be ~flat

11. 1 +- and 2 -- can rule out 1 +- (Cl=10 -4 %) 2 -- is unlikely (CL=0.16%) |cos  J/  | 1 +- : sin 2  J/  2 -- : sin 2  J/  cos 2  J/   2 /dof=36/9  2 /dof=27/9 |cos  J/  |

12. 0 -+ Rosner (PRD 70 094023) 0 -+ : sin 2  sin 2  safe to rule out 0 -+    2 /dof=31/9 |cos  | |cos  |  2 /dof=61/9

13. 0 ++ Rosner (PRD 70 094023) again ll In the limit where X(3872), , & J/  rest frames coincide: d  /dcos  l   sin 2  l  |cos  l  | rule out 0 ++  2 /dof = 59/9

14. 1 ++ ll  1 ++ : sin 2  l sin 2  K 1 ++ looks okay! compute angles in X(3872) restframe |cos  l |  2 /dof = 10.4/9 |cos  |  2 /dof = 8.1/9 Rosner (PRD 70 094023)

15. 1 ++ again compute  in  rest frame compute  in J  rest frame  2 /dof = 8.9/9 |cos  l ||cos  |

16. Reduce type size for J PC values that fail angle tests 0 - - exotic violates parity 0 -+ (  c ” ) 0 ++ DD allowed (  c0 ’ ) 0 +- exotic DD allowed 1 - - DD allowed (  (3S)) 1 -+ exotic DD allowed 1 ++ (  c1 ’ ) 1 +- (h c ’ ) 2 - - (  2 ) 2 - + (  c2 ) 2 ++ DD allowed  c2 ’ ) 2 +- exotic DD allowed

17. Observation of X(3872)   J/ 

18. Select B  K J/   (include both K ± & K s ) Tight J/  cuts K ± id>0.5 / Belle-standard “good Ks” E  >40 MeV  0 veto (  2 >4.0) K* veto (M(K  )>1.0 GeV) R 2 <0.4; |cos  B | < 0.8 |M bc – 5.28|<0.0055 GeV (2  ) |  E|<0.034 GeV (2  ) E7  E37

19. M(  J/  ) X signal Region ± 32 MeV M(  J/  ) B  K  c1 ;  c1   J/  X(3872)?

20. N ev (  c1 ) = 653 ± 26 |M(  J/  ) – m  c1 | < 25 MeV ( ± 2.4  ) Expand  c1 region Fit to determine  M(  J/  ) =10.7 MeV Use these fits to get means & sigmas for M bc and  E

21. M(  J/  ) in X(3872) region No signif. peaking bkgnd scaled fit: 1.0 ± 2.1 evts Signif =  2ln L (1.0) -2ln L (13.4) = 5.1  ± 32 MeV Use this fit to get Efact for ARGUS sideband N ev (X 3872 ) = 13.4 ± 4.4 X(3872)

22. Br(X   J/  ) determination Br(X   J/  ) Br(X      J/  ) = N ev (X   J/  ) N ev (  c1   J/  ) N ev (X       J/  ) N ev (  ’       J/  )  Br(B  K  c1 )Br(  c1   J/  ) Br(B  K  ’ ) Br(  ’      J/  )  (  c1   J/  )  (  ’   J/  )  (  ’       J/  )  (X       J/  )  data: 0.30 ± 0.11 from PDG 1.02 ± 0.22 ~1.02± 0.10 = 0.30 ± 0.11 ± 0.06 (Previous 90% CL upper limit was <0.4)

23. Evidence for C=+1 is becoming overwhelming B   J/  only allowed for C=+1 same for B  ”  ”J/  (reported earlier) M(  ) for X      J/  looks like a  X   J/  (  -J/  in an S-wave)  2 /dof=35/39 X   J/  (  -J/  in an S-wave)  2 /dof=63/39

24. C = -1 is ruled out reduce typesize of C=-1 entries 0 - - exotic violates parity 0 -+ (  c ” ) 0 ++ DD allowed (  c0 ’ ) 0 +- exotic DD allowed 1 - - DD allowed (  (3S)) 1 -+ exotic DD allowed 1 ++ (  c1 ’ ) 1 +- (h c ’ ) 2 - - (  2 ) 2 - + (  c2 ) 2 ++ DD allowed  c2 ’ ) 2 +- exotic DD allowed

25. Remaining states 1 ++  & J/  in an S-wave 2 -+ “ “ a P-wave

26. Fits to the M(  ) Distribution X   J/  in P-wave has a q* 3 centrifugal barrier X J/   q*

27. M(  ) can distinguish  -J/  S- & P-waves S-wave:  2 / dof = 35/39 P-wave:  2 / dof = 80/39 q* roll-off q* 3 roll-off (CL=0.014%) (CL= 67%) Shape of M(  ) distribution near the kinematic limit favors S-wave

28.  -J/  in a P-wave is unlikely reduce type-size of all J -+ entries 0 - - exotic violates parity 0 -+ (  c ” ) 0 ++ DD allowed (  c0 ’ ) 0 +- exotic DD allowed 1 - - DD allowed (  (3S)) 1 -+ exotic DD allowed 1 ++ (  c1 ’ ) 1 +- (h c ’ ) 2 - - (  2 ) 2 - + (  c2 ) 2 ++ DD allowed  c2 ’ ) 2 +- exotic DD allowed

29. “The one which remains:” 1 ++ (passes all the tests) |cos  l |  2 /dof = 10.4/9 |cos  |  2 /dof = 8.1/9 M(     )  2 /dof = 35/39 & consistent with observations of: X   J/  X  ”  ” J/ 

30. Could the X(3872) be the  c1 ’ ?  (2 3 P 1   J/  ) ~ 11 keV  (2 3 P 1   J/  ) ~  (  ’    J/  ) ~ 0 (0.3 keV) ~30 isospin violating Barnes, Godfrey hep-ph/0311162 Rough expectation for pure charmonium: we measure 0.3; two orders-of-magnitude smaller;   c1 ’ component of the X(3872) must be small Mass is way off: 3872 vs 3929  3990 MeV Br(X   J/  ) = 0.3 is much too small theory range

31. Summary We learn a lot from angular distribs with ~50 evts –Rule out 0 -+, 0 ++, 1 -- and 1 +- ; 2 – is unlikely (CL~0.16%) B   J/  (plus “  ”J/  M(  )) rules out all C=-1 M(  ) favors S-wave  -J/  (P-wave CL=0.014%) –Rules out 2 -+, 1 -+ & 0 -+ Only 1 ++ passes all tests –angular distributions & M(  ) fitted well –  c1 ’ assignment unlikely (Br(  J/  ) is too small) –DD* molecule models favor 1 ++ Tornqvist hep-ph/0308277 Swanson PLB588, 189(2004)

32. plan Generate MC for each J PC –compare MC distributions with data Search for X   ’  (theory for  c1 ’: ~ 6x  J/  ) PRD on X(3872) properties? –angular studies –other decay modes X   J/    include e39 data? X  DD, DD* ??,  separate paper? X  3  J/   include e39 data? – M(  ) fits

33. Back-up slides

34. Q: why not do 2-d fits for angular distributions? A: We are not measuring parameters, we doing hypothesis testing, & so, we need a binned  2. With < 50 events, 2-dim binning with reasonable bin sizes will have ≤1event/bin.

35. Q: Is the M(  J/  ) look-back plot consistent with a 10.5 evt X   J/  signal? A: YES (yield fixed at value from M bc -  E fit;  scaled from  c1   J/  peak) 13.4 evt Signal